# Solids Of Revolution

### #1

Posted 04 February 2010 - 03:28 PM

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

### #2

Posted 06 February 2010 - 02:06 AM

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

### #3

Posted 06 February 2010 - 09:24 PM

In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)

Y(s,t) = sin(t) * f(s)

Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

### #4

Posted 07 February 2010 - 03:39 AM

Is this what you need?

In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)

Y(s,t) = sin(t) * f(s)

Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

### #5

Posted 07 February 2010 - 08:11 PM

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!

Nope, as far as I know, you can't even draw several surfaces at once.

### #6

Posted 07 February 2010 - 11:38 PM

Nope, as far as I know, you can't even draw several surfaces at once.

Hi Kilburn, me again. Isn't there some way to generate and store a surface, and then generate the second surface and store it, and then simply display both? If that was possible, it would be totally awesome!

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